how do you solve sec(arccot(-1))

Question

 need help solving this.

Answer 1

Work this type of problem from the inside out.  First, find the angle whose cotangent is -1.  Then evaluate the secant of that angle.  There are 2 angles whose cotangent is equal to  -1.  They are 135° and 315°.  Test them.  Next, take the secant of the angle, which is just the reciprocal of the cosine.